abstract

We consider Hamiltonian systems with spatially varying effective mass and slowly varying local potential in \(d\) dimensions. The Slater sum is defined as the diagonal element of the Bloch propagator. We derive a gradient expansion of the Slater sum up to the second order. We will show that the derived analytical expression is valid for \(d=1,2,3\) and\(\ 4\). A numerical example is shown to highlight the effect of the spatially varying effective mass.

abstract

We provide the quantum mechanics of many particles moving in twisted \(N\)-enlarged Newton–Hooke space-time. In particular, we consider the example of such noncommutative system — the set of \(M\) particles moving in Coulomb field of external point-like source and interacting each other also by Coulomb potential.

abstract

In this paper, we point out that the analytic solution of the two dimensional U\((1)\) gauge theory, on a finite lattice, reveals in the continuum limit the renowned Manton’s spectrum of topological electric fluxes together with their effective Hamiltonian and wave functions. We extend this result for the system with strings and external charges providing also a novel interpretation of the \({\mit \Theta }\) parameter. Some further generalizations are also outlined.

abstract

Hosotani mechanism in higher-dimensional Lee–Wick theory is investigated. The symmetry breaking mechanism proposed by Hosotani is studied at one-loop level through a toy model in this theory. We find that the phase diagram of symmetry and masses of fields are modified from the original ones if masses of Lee–Wick particles are in the same order of the inverse of the compactification scale.

abstract

The supersymmetric standard model undergoes parity violation in QCD through chiral quark–squark–gluino interactions with non-degenerate masses between left-handed and right-handed squarks. A bound for the mass degeneracy between left-handed and right-handed squarks should exist, since experiments have not shown any parity violation in QCD yet. In this paper, we establish methods of analysis to estimate this bound for each squark. Firstly, we investigate a non-degeneracy bound between \(m_{\tilde {c}_{\rm L}}\) and \(m_{\tilde {c}_{\rm R}}\) from experimental data of charmonium decay. Secondly, we evaluate the non-degeneracy bounds for \(\tilde {u}\) and \(\tilde {d}\) from nucleon–meson scattering data, and comment on other squarks. Unfortunately, our results are below current experimental data, and cannot obtain the left–right degeneracy bounds for squark masses. However, we hope that our method is useful for obtaining bounds from future experimental data and research of an origin of parity violation.

abstract

We address aspects of jet physics at the Large Hadron Collider, focusing on features of recent jet measurements which challenge the theory. We discuss examples illustrating the role of QCD parton showers, nonperturbative corrections, soft multi-gluon emission.

abstract

Masses of the heaviest deformed even–even nuclides with the atomic number \(Z=98\)–114 have been calculated by applying a macroscopic–microscopic method. Approximate formulas for calculating masses of odd and odd–odd nuclides from the calculated masses of the neighboring even–even nuclides and the average pairing energies of unpaired nucleons are used. For the 56 heaviest deformed nuclides, for which masses are experimentally known, the standard deviation of 0.30 MeV has been obtained.

abstract

A new, unorthodox mechanism is proposed to explain the formation of kimberlite pipes supposed to have been formed as the result of cosmic ultra-dense objects (CUDO) passing through the Earth. Moreover, it is proposed that due to such a passage, neutrons produced in nuclear reactions in the plasma formed at the front of passing objects, cause natural elements abundances and their isotopic ratios to change. Thus, to assess our model and hopefully obtain an indirect proof to CUDO class objects existence, we suggest researching such geochemical anomalies in crustal country rocks around kimberlite pipes, as well as in xenoliths embedded in kimberlite materials.